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Rational Numbers on the Number Line

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Examples, solutions and worksheets to help Grade 6 students learn about rational numbers on the number line.

New York State Common Core Math Grade 6, Module 3, Lesson 6

Worksheets for Grade 6

Lesson 6 Student Outcomes

Students use number lines that extend in both directions and use 0 and 1 to locate integers and rational numbers on the number line. Students know that the sign of a nonzero rational number is positive or negative, depending on whether the number is greater than zero (positive) or less than zero (negative), and use an appropriate scale when graphing rational numbers on the number line.

Students know that the opposites of rational numbers are similar to the opposites of integers. Students know that two rational numbers have opposite signs if they are on different sides of zero, and that they have the same sign if they are on the same side of zero on the number line.

What is a rational number?

A rational number is a number that can be written as a fraction.
A decimal is rational if it terminates or repeats with a pattern.

Opening Exercises

1. Write the decimal equivalent of each fraction.
a. 1/2
b. 4/5
c. 6 7/10

2. Write the fraction equivalent of each decimal.
a. 0.42
b. 3.75
c. 36.90 Example 1: Graphing Rational Numbers

If b is a nonzero whole number, then the unit fraction 1/b is located on the number line by dividing the segment between 0 and 1 into b segments of equal length. One of the b segments has 0 as its left endpoint; the right endpoint of this segment corresponds to the unit fraction 1/b

Locate and graph the number 3/10 and its opposite on the number line.

Exercise 1

Use what you know about the points - 7/4 and its opposite to graph both points on the number line below. The fraction, - 7/4, is located between which two consecutive integers? Explain your reasoning.

Example 2: Rational Numbers and the Real World

The water level of a lake rose 1.25 feet after it rained. Answer the questions below using the diagram below.

a. Write a rational number to represent the situation.

b. What two integers is 1.25 between on a number line?

c. Write the length of each segment on the number line as a decimal and a fraction.

d. What will be the water level after it rained? Graph the point on the number line.

e. After two weeks of rain, the water level of the lake is the opposite of the water level before it rained. What will be the new water level? Graph the point on the number line. Explain how you got your answer.

f. State a rational number that is not an integer whose value is less than 1.25 , and describe its location between two consecutive integers on the number line.

Problem Set
1. In the space provided, write the opposite of each number.
a. 10/7
b. -5/3
c. 3.82
d. -6 1/2

2. Choose a non-integer between 0 and 1. Label it point A and its opposite point B on the number line. Write values below the points.
a. To draw a scale that would include both points, what could be the length of each segment?
b. In words, create a real-world situation that could represent the number line diagram.

3. Choose a value for point P that is between -6 and -7.
a. What is the opposite of point P?
b. Use the value from part (a), and describe its location on the number line in relation to zero.
c. Find the opposite of the opposite of point P. Show your work, and explain your reasoning.

4. Locate and label each point on the number line. Use the diagram to answer the questions.
Jill lives one block north of the pizza shop.
Janette’s house is 1/3 block past Jill’s house.
Jeffrey and Olivia are in the park 4/3 blocks south of the pizza shop.
Jenny’s Jazzy Jewelry Shop is located halfway between the pizza shop and the park.
a. Describe an appropriate scale to show all the points in this situation.
b. What number represents the location of Jenny’s Jazzy Jewelry Shop? Explain your reasoning.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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